Question

I’m a beginner so I’m probably confused on some fundamental level, but I seem to get the same result with the following two Draw() routines and I’m wondering is there any difference and is one more correct than the other?

In one I apply transformation to the world matrix and in the other I apply transformation to the veiw matrix. I think the result is exactly the same but I’m not 100% sure.

    protected override void Draw(GameTime gameTime)
    {
        GraphicsDevice.Clear(Color.CornflowerBlue);

        Matrix worldMatrix =
            Matrix.CreateTranslation(view.Position.X, view.Position.Y, view.Position.Z) *
            Matrix.CreateRotationX(view.Rotation.X) *
            Matrix.CreateRotationY(view.Rotation.Y) *
            Matrix.CreateRotationZ(view.Rotation.Z);

        Matrix viewMatrix = Matrix.CreateLookAt(view.CameraPosition, view.CameraTarget, view.CameraUp);

        Matrix projectionMatrix = Matrix.CreatePerspectiveFieldOfView(view.FieldOfView,
                                                                      GraphicsDevice.Viewport.AspectRatio,
                                                                      view.NearPlane,
                                                                      view.FarPlane);

        DrawModels(worldMatrix, viewMatrix, projectionMatrix);

        base.Draw(gameTime);
    }

How’s that different from:

    protected override void Draw(GameTime gameTime)
    {
        GraphicsDevice.Clear(Color.CornflowerBlue);

        Matrix worldMatrix = Matrix.Identity;

        Matrix viewMatrix =
            Matrix.CreateTranslation(view.Position.X, view.Position.Y, view.Position.Z) *
            Matrix.CreateRotationX(view.Rotation.X) *
            Matrix.CreateRotationY(view.Rotation.Y) *
            Matrix.CreateRotationZ(view.Rotation.Z) *
            Matrix.CreateLookAt(view.CameraPosition, view.CameraTarget, view.CameraUp);

        Matrix projectionMatrix = Matrix.CreatePerspectiveFieldOfView(view.FieldOfView,
                                                                      GraphicsDevice.Viewport.AspectRatio,
                                                                      view.NearPlane,
                                                                      view.FarPlane);

        DrawModels(worldMatrix, viewMatrix, projectionMatrix);

        base.Draw(gameTime);
    }

Answer 1

Matrix multiplication is associative: (A*B)C = A(B*C),
but not commutative: AB != BA for every matrix. Thus, if DrawModels multiplies the matrices world, view and projection from left to right, then the two methods give exactly the same results (+- rounding errors…).

It’s purely a design issue, how the matrices are decomposed or concatenated. E.g. premultiplying viewMatrix and projectionMatrix can make sense — IIRC viewMatrix * symmetric_projectionMatrix introduces just 4 or 5 extra multiplications to the generation of the viewMatrix from 3 Euler angles or quaternion camera representation. Doing the multiplication for generic 4×4 matrices takes 64 multiplications…

One thing to consider is how to cull bounding boxes — either axis aligned, or generic. This can be done in world space, camera space or clip space. Which ever makes most sense should dictate how the matrices are premultiplied.